Persona • AI Writing Assistant

Mathematician persona: LaTeX-ready proofs, lectures, and reproducible examples

Draft clean proofs, convert text to compiled LaTeX with numbered environments, generate lecture notes and problem sets, and produce executable examples (SymPy/Jupyter). Choose the level of rigor and receive verification checklists tailored to mathematical writing.

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Capabilities

What the mathematician persona does

This persona is designed for mathematicians, instructors, and technical writers who need precise, verifiable math content. It prioritizes consistent notation, explicit assumptions, and stepwise reasoning. Outputs can be tailored for classroom use, research drafts, submissions, or formal-verification workflows.

LaTeX-ready proofs with theorem/lemma/corollary environments and numbered equations.
Lecture plans (45–60 minutes) with definitions, examples, exercises, and suggested reading.
Problem sets across multiple difficulty tiers with solutions and grading notes.
Reproducible code snippets (SymPy/Jupyter) demonstrating computations and examples.
Formal-verification outlines that map arguments into lemmas and definitions suitable for Lean or Coq adaptation.

Practical prompts

Prompt clusters and ready-to-use templates

Use these concise prompt templates to get results aligned with common mathematical workflows. Each prompt can request output format (LaTeX, plain text, markdown), level of rigor, and accompanying runnable examples.

Proof sketch

Concise overview emphasizing key lemmas and dependencies.

Prompt: "Given statement S, produce a concise sketch highlighting core lemmas, required assumptions, and the high-level strategy."
Use when you need a quick roadmap before writing a full proof.

Full pedagogical proof

Step-by-step proof with intuition and references.

Prompt: "Write a step-by-step proof suitable for a graduate seminar; include intuition, key references, and numbered equations in LaTeX."
Good for lecture notes and seminar handouts.

Formal-verification outline

Structure an argument for porting to proof assistants.

Prompt: "Translate this argument into a sequence of clearly stated lemmas and definitions that can be adapted for Lean/Coq, listing dependencies and types."
Helps accelerate formalization work by producing a scaffolding document.

LaTeX conversion

Turn plain text math into compiled-ready LaTeX.

Prompt: "Convert the following proof into compiled-ready LaTeX with amsthm environments, numbered theorems, and displayed equations."
Outputs suitable for Overleaf and journal submissions.

Problem set generator

Create graded exercises with solutions and grading notes.

Prompt: "Create 8 problems across beginner/intermediate/advanced tiers with full solutions, approximate time per problem, and grading rubrics."
Use for assignments and exam prep.

Reproducible example

Provide Jupyter/SymPy-ready code that corresponds to the math.

Prompt: "Provide a SymPy/Jupyter-ready snippet that demonstrates the computation or example, with comments and expected numeric output."
Useful for notebooks accompanying lecture notes or papers.

Who benefits

How it helps different users

Designed for people who need both mathematical precision and practical export formats. Below are typical workflows and outcomes.

Research mathematicians: draft polished proofs, prepare submission-ready LaTeX, and get a formalization outline for proof assistants.
Graduate students and postdocs: generate lecture-ready explanations, homework sets, and reproducible examples for reproducibility sections.
Instructors: design lecture plans and graded assignments with clear solutions and grading notes.
Quantitative researchers and technical writers: translate formal math into readable narrative and executable demonstrations.

References & tools

Source ecosystem and verification

The persona is intended to be used alongside standard mathematical resources and tooling. For rigorous verification, combine AI output with bibliographic checks and symbolic or formal tools.

Use arXiv summaries and MathSciNet/zbMATH to locate primary references and citation context.
Cross-check computations with SymPy or WolframAlpha and include the code used for verification.
When formal rigor is required, adapt the outline for Lean/Coq and run proofs through the chosen proof assistant.
Consult community Q&A (MathOverflow/StackExchange) to spot standard counterexamples and edge cases.

Output options

Export formats & integration

Exportable outputs reduce manual rework and integrate into common authoring tools.

LaTeX: theorem/lemma environments, numbered equations, BibTeX-ready citation placeholders.
Markdown or plain text for notes and blog-friendly summaries.
Jupyter/SymPy snippets with comments and expected outputs for reproducibility.
Formalization outline that lists definitions, lemma statements, and suggested types for porting to Lean/Coq.

Responsible use

Safety, integrity, and academic use

The assistant can generate homework and exam-style problems; instructors should apply standard academic integrity policies. Use outputs as drafting and teaching aids and verify proofs and code before grading or publishing.

Mark AI-generated material where required by your institution’s policy.
Treat proofs as draft artifacts to be independently checked and peer-reviewed.
Use counterexample prompts and the proof-check checklist before submission.

FAQ

How reliable are proofs produced by the mathematician persona and how should I verify them?

AI-generated proofs are a drafting aid, not a substitute for formal verification or peer review. Verify proofs by: 1) checking every inference against definitions and standard theorems, 2) running symbolic checks or computations (SymPy, WolframAlpha) where applicable, 3) attempting to construct counterexamples using the counterexample-finder prompt, and 4) adapting the argument into a formal-verification outline and validating it in Lean or Coq if full formal assurance is required.

Can the assistant output publication-ready LaTeX and numbered theorem environments?

Yes — request compiled-ready LaTeX output and specify the document class or amsthm conventions you prefer. The assistant will format theorem/lemma/corollary environments and numbered equations, and can include BibTeX citation placeholders for you to complete with verified bibliographic entries.

What level of rigor can I request (sketch vs full formal proof vs classroom explanation)?

You can request multiple rigor levels: a brief sketch highlighting key ideas, a detailed pedagogical proof with intuition and steps, or a formal-verification-style outline that lists lemmas and definitions suitable for porting to proof assistants. Specify the desired level in your prompt and include audience (e.g., graduate students, journal referees) to tune tone and depth.

How do I get reproducible code examples (SymPy/Jupyter) that match the written math?

Ask for Jupyter/SymPy-ready snippets and request expected outputs and comments. After receiving the snippet, run it locally or in a notebook to validate numeric results. For symbolic identities, cross-check with SymPy simplify/expand routines and attach the verification steps to your notes or submission.

Is the persona suitable for generating homework or exam problems — how to avoid academic integrity issues?

The persona can generate problem sets and solutions for instructors. To avoid integrity issues, follow your institution’s policies: disclose use of AI where required, modify generated questions to match your course style, and use the persona primarily as a drafting tool rather than a source of unvetted exam content.

Can the assistant suggest relevant literature and format citations in BibTeX?

Yes — the assistant can suggest likely primary references (arXiv entries, classic texts) and produce BibTeX-formatted entries as placeholders. Always verify bibliographic details (authors, titles, DOIs) against primary sources such as arXiv, MathSciNet, or publisher pages before final submission.

How do I adapt an AI-generated proof for formal verification tools like Lean or Coq?

Request a formal-verification outline that breaks the argument into definitions, lemma statements, and dependency order. Use the outline as a roadmap: encode definitions and lemmas in the proof assistant, attempt small lemmas first, and iteratively refine the formal version. The assistant can suggest tactics or library imports commonly used in Lean/Coq workflows, but final formalization requires specialist review.

What privacy or IP considerations should I keep in mind when drafting unpublished proofs?

Treat unpublished proofs and confidential research as sensitive. Follow your organization’s data and IP policies before submitting content to any external AI service. Keep master copies offline and use the assistant to draft text that you then vet and store in your secure repositories.

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